For hydrogen atoms, all book take correction up to 1/c^2 where the perturbation is -P^4/8*m^3*c^2. And they go solving it by sandwiching p^4 term where they consider p^2 = 2m*(1+e^2/r). and they square it to solve for p^4.(adsbygoogle = window.adsbygoogle || []).push({});

To get a better view of perturbation to first order please see attachment.

What if I want it to the second order correction, that is to p^6? The additional perturbative term would be p^6/16*m^5*c^4. What should be done in this case?

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# Relativistic Correction

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